The invention relates to a method for connection establishment and a radio system relaying packet traffic. A terminal informs the system that it wishes to transmit data. The network part receives the message and allocates default radio resources and informs the allocated resources to the terminal. The terminal sends a first control message to inform the terminal's radio path characteristics. According to the solution of the invention, when allocating the default amount of radio resources to the terminal, the network part is arranged to reserve one or more radio blocks for the terminal's control messages. When the terminal sends the network part information about its radio path characteristics, it is arranged to inform in the message if there are additional characteristics. In that case, the terminal sends a second control message including information about its radio path characteristics.